Volatility as a risk measure has been criticized and dismissed on various grounds. Yet, volatility is the dominating risk measure in the investment management industry. Volatility is typically calculated as the arithmetic standard deviation of returns. At the same time, it is industry practice...

We discuss the problems associated with changing individual correlation values in a valid correlation matrix and outline a solution for calculating upper and lower bounds within which correlations can be modified, such that the resulting correlation matrix is still valid. We illustrate two...

We highlight important and specific characteristics of default risk and methodological implications. In a simulation contrasting independent, Gaussian and Clayton copulas, we also show that joint default probabilities might be a hidden source of risk in conventional portfolio models of default

Correlations play an important role in the construction of investment portfolios. In this research note, we explain why the manipulation of a valid correlation matrix is challenging. We also propose three methods to perform the following tasks: 1) Increase all correlations such that they...

Portfolio theory got it all wrong: asset weights are not decision variables, because security prices a portfolio manager does not have full control over asset prices. In this note, we are trying to create awareness that real-valued allocations which have been calculated from numerical portfolio...

Ex post volatility is defined as dispersion of ex post portfolio returns over the measurement period. Ex post volatility takes into account the variability in asset returns and changes of asset weights over time due to trading and drift. Ex ante volatility, on the other hand, is defined as...

We explain the variability of the mean-variance efficient frontier over time with a statistical three factor model. For an asset universe consisting of 22 stocks listed in Switzerland, the model explains more than 99% of the time variations in the efficient frontier.The three factors can be...